Problem: Solve for $x$, ignoring any extraneous solutions: $\dfrac{x^2}{x - 2} = \dfrac{x + 30}{x - 2}$
Solution: Multiply both sides by $x - 2$ $ \dfrac{x^2}{x - 2} (x - 2) = \dfrac{x + 30}{x - 2} (x - 2)$ $ x^2 = x + 30$ Subtract $x + 30$ from both sides: $ x^2 - (x + 30) = x + 30 - (x + 30)$ $ x^2 - x - 30 = 0$ Factor the expression: $ (x + 5)(x - 6) = 0$ Therefore $x = -5$ or $x = 6$